A few days after the semester started, Zhao Xiancai contacted Dean Yang and told him that he had decided on the direction and topic of his undergraduate research.

"What? Are you going to study Abelian expansion? Your first paper was about differential equations, and your second paper was about number theory and combinatorics. Why are you starting to study class field theory again?

I'm attending a meeting outside now, and I'm not in the capital either. You can briefly tell me your thoughts first, and we'll talk in person after I go back in a few days."

After hearing Zhao Xiancai say that he was going to study the issue of Abelian expansion, Yang Gang was shocked. Zhao Xiancai had too many ideas. One paper researched one direction.

"That's right, when I was at home during the winter vacation..."

Zhao Xiancai briefly explained to Dean Yang on the phone why he chose to study Abel's expansion.

"That's it?"

After hearing what Zhao Xiancai said, Dean Yang was even more confused. He thought Zhao Xiancai had some unique ideas, but who would have thought that for just such a reason, he would choose to study the issue of Abel's expansion.

"That's it."

"Is it gone?"

"Gone."

"..."

Dean Yang didn't know what to say for a moment. This was the first time he had seen a student like Zhao Xiancai.

Zhao Xiancai is now used to this kind of situation. He added: "It was the same when I studied Erdős's arithmetic sequence conjecture last time."

"Last time, you had just such an idea and then put it into action?" Dean Yang asked after hearing what Zhao Xiancai said.

"Yes." Zhao Xiancai confirmed again.

After another moment of silence, Dean Yang continued to speak: "Okay, I will come to you for other matters after I go back, and I will also arrange a tutor for you. I have some things to be busy with here, first

Bye."

After saying that, Dean Yang hung up the phone.

Zhao Xiancai, on the other hand, took advantage of the few days that Dean Yang was away to take the TOEFL to prepare for his future trip abroad.

The TOEFL test is an academic English language test developed by ets assessment. It tests the four skills of listening, speaking, reading and writing to reflect the participants' real academic language ability in the academic language task environment, and can be used for undergraduate students.

and postgraduate school applications.

When domestic students studying abroad take the English test, they usually take one of two tests, namely TOEFL and IELTS, which are the two most common language tests for studying abroad.

The biggest difference between them is that IELTS is mainly suitable for studying in Commonwealth countries, while TOEFL is suitable for North American countries, but now some North American universities also accept IELTS.

A few days later, Dean Yang finally returned to the capital.

As soon as Dean Yang returned to Peking University, he sent a message to Zhao Xiancai, asking him to go to his office tomorrow morning to talk about his undergraduate thesis.

When Zhao Xiancai received the news from Dean Yang, he went to Dean Yang's office the next day.

"This is Academician Wang Shicheng, Academician Wang, he is Zhao Xiancai."

When Zhao Xiancai arrived at the dean's office, he discovered that there was not only the dean in the dean's office today, but also an old professor who should be about the same age as Dean Yang.

After listening to Dean Yang's introduction, Zhao Xiancai said to Academician Wang: "Hello, Academician Wang."

"You don't have to be so polite. Since I am your mentor now, you can just call me mentor or teacher. I heard from Dean Yang that you are going to study the problem of Abelian expansion structures in the whole real domain?"

Academician Wang asked Zhao Xiancai.

"Yeah." Zhao Xiancai nodded somewhat uneasily and responded.

"I also study problems such as group theory and algebraic number theory, and I have some understanding of this aspect.

Although this problem has been worked on generation after generation, many breakthroughs have been made so far. Especially after the p-adic l function was constructed, it has brought powerful tools to analytic number theory and algebraic number theory.

However, if you take this as your undergraduate thesis, I’m afraid you won’t be able to graduate this year,” said Academician Wang.

"Wang Yuan...Teacher, I'm not saying that I plan to solve this problem when I'm an undergraduate, but I plan to publish a paper after I get some results in the research process, and treat this paper as my undergraduate graduation thesis.

" Zhao Xiancai explained.

"Have we achieved some results? I'm afraid this is not a simple matter. There are only more than three months left before June.

If you can't come up with a thesis when graduation is about to happen, your graduation will be delayed."

Academician Wang kindly advised.

"Thank you for your concern, teacher. I will pay attention to this." Zhao Xiancai said.

Seeing that Zhao Xiancai had no intention of backing down or changing his mind, Academician Wang stopped persuading Zhao Xiancai and said to him: "In that case, I won't say anything more. If you have any questions during the research process,

If you don’t understand anything, you can ask me at any time.

If I don't have time or I'm not in school, you can also find those senior fellow students with Ph.D.s, and I will pull you into the group in a while.

I don’t know whether you are going to realize Stark’s conjecture through p-adic l function, or are you going to find another way?”

At the end of the conversation, Academician Wang also asked Zhao Xiancai what he thought.

"It's not decided yet." Zhao Xiancai said truthfully.

Academician Wang and Dean Yang looked at each other, and they both saw speechless expressions in each other's eyes.

"If you are not sure yet, as your mentor, I still recommend that you use the p-adic l function to realize Stark's conjecture.

Since be hyman gross, most of the Stark conjectures have taken the path of p-adic l functions, so this path now seems to be the path closest to the end.

[The book-chasing app recommended to me by an old book friend who I have known for ten years is the Changyuan app! It is so easy to use. I rely on this to read and listen to books while driving and before going to bed. You can download it here. huanyuanapp ]

However, if you are really prepared to study this, you must be mentally prepared to continue studying it for the next ten or twenty years, or even longer."

"Thank you, teacher, for your advice." Zhao Xiancai also expressed his gratitude for Dean Wang's advice.

After saying this to Zhao Xiancai, Academician Wang looked at Dean Yang aside and said to him: "I have almost finished talking about my affairs. You can tell him about the things that the school has arranged for him. Look at himself.

What do you think?"

Hearing what Academician Wang said to Dean Yang, Zhao Xiancai also looked at Dean Yang with some curiosity. Could it be that they asked him to come here for some other reason?

"Well." Dean Yang nodded to Dean Wang first, and then said to Zhao Xiancai, "Xiao Zhao, it's like this. The school has specially formulated a training plan for you. This plan will not delay your going to Princeton University.

Further study.

Well, the school and Princeton University have also communicated and decided to jointly train you.

Didn’t you complete your undergraduate degree at Beijing University?

After that, you can go to Princeton University to study for a PhD as usual. We will cover all your tuition fees, living expenses, etc., and after you complete your studies there, you can come back and get a PhD from Peking University.

and diploma.”

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